An Effective Characterization of the Alternation Hierarchy in Two-Variable Logic

被引：2

作者：

Krebs, Andreas ^{[1
]}

Straubing, Howard ^{[2
]}

机构：

[1] Univ Tubingen, Wilhelm Schickard Inst, Sand 13, D-72076 Tubingen, Germany

[2] Boston Coll, Comp Sci Dept, Chestnut Hill, MA 02467 USA

来源：

ACM TRANSACTIONS ON COMPUTATIONAL LOGIC | 2017年 / 18卷 / 04期

关键词：

FO2; Quantifier Alternation; J; Pseudovarities; Identities; CATEGORIES;

D O I：

10.1145/3149822

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We give an algebraic characterization, based on the bilateral semidirect product of finite monoids, of the quantifier alternation hierarchy in two-variable first-order logic on finite words. As a consequence, we obtain a new proof that this hierarchy is strict. Moreover, by application of the theory of finite categories, we are able to make our characterization effective: that is, there is an algorithm for determining the exact quantifier alternation depth for a given language definable in two-variable logic.

引用

页数：22

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